Many optical communication systems manipulate light waves to carry information. For instance, often a light source (e.g., a laser source) is modulated to change various properties of emitted light, such as an amplitude, phase, or frequency of the light to convey information. Phase modulation, also called phase shift keying (PSK), is a commonly used communications technique in which information, in symbols, is encoded onto a carrier signal using phase changes. Phase shift modulation provides log2(2N) bits per symbol, where N is the number of symbols in the complex signal plane. For example, binary phase shift keying (BPSK) has two symbols or one bit per symbol. Quadrature phase shift keying (QPSK) has four symbols or two bits per symbol.